Subgroups — C₂×#19148494 #26005091

Order 11008.

7302 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148494	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583631	C₂	1	4	yes	maximal, complemented
3	C₂×#14583623	C₂	1	4	yes	maximal, complemented
4	C₂×#14583572	C₂	1	8	yes	maximal, complemented
5	C₂×#14583522	C₂	1	4	yes	maximal, complemented
6	C₂×#14583463	C₂	1	1	yes	maximal, characteristic
7	C₂×#14583452	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14583435	C₂	1	4	yes	maximal, complemented
9	C₂²×#13063314	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14583377	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14583373	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583631	C₂²	1	64	yes	complemented
16	#14583623	C₂²	1	64	yes	complemented
17	#14583572	C₂²	1	128	yes	complemented
18	#14583522	C₂²	1	64	yes	complemented
19	#14583463	C₂²	1	16	yes	—
20	#14583452	C₂²	1	16	yes	complemented
21	C₂×#13063324	C₂²	1	2	yes	complemented
22	C₂×#13063321	C₂²	1	2	yes	—
23	#14583435	C₂²	1	64	yes	complemented
24	C₂×#13063320	C₂²	1	8	yes	complemented
25	C₂×#13063320	C₂²	1	8	yes	complemented
26	C₂×#13063316	C₂²	1	2	yes	complemented
27	C₂×#13063314	C₂²	1	2	yes	—
28	C₂×#13063314	C₂²	1	4	yes	—
29	C₂×#13063314	C₂²	1	2	yes	—
30	C₂×#13063314	C₂²	1	2	yes	—
31	C₂×#13063314	C₂²	1	16	yes	complemented
32	C₂×#13063311	C₂²	1	8	yes	complemented
33	C₂×#13063309	C₂²	1	8	yes	complemented
34	C₂×#13063307	C₂²	1	8	yes	complemented
35	C₂×#13063305	C₂²	1	8	yes	complemented
36	C₂×#13063302	C₂²	1	4	yes	—
37	C₂×#13063299	C₂²	1	4	yes	—
38	C₂×#13063293	C₂²	1	4	yes	—
39	#14583377	C₂²	1	16	yes	complemented
40	#14583373	C₂²	1	16	yes	complemented
41	#41×Dic₄₃	C₂²	1	16	yes	complemented
42	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	complemented
43	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	complemented
44	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	complemented
45	C₂×C₄×Dic₈₆	C₂²	1	4	yes	complemented
46	C₂×C₄×D₁₇₂	C₂²	1	4	yes	—
47	C₂×D₄×Dic₄₃	C₂²	1	4	yes	—
48	C₂×D₄×Dic₄₃	C₂²	1	2	yes	complemented
49	C₂×#13063287	C₂²	1	4	yes	—
50	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	8	yes	complemented
51	C₂×#13063284	C₂²	1	1	yes	characteristic
52	C₂×#13063284	C₂²	1	4	yes	—
53	C₂×#13063284	C₂²	1	1	yes	characteristic
54	C₂×#13063284	C₂²	1	2	yes	complemented
55	C₂×#13063283	C₂²	1	8	yes	complemented
56	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
57	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
58	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	complemented
60	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
61	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
62	C₄₃×#536	C₂²	1	16	yes	complemented
63	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
64	C₂×#124×C₄₃	C₂²	1	2	yes	complemented
65	C₂×#123×C₄₃	C₂²	1	4	yes	—
66	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
67	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
68	C₂⁴×D₄₃	C₂³	1	2	yes	—
69	C₂²×Dic₈₆	C₂³	1	4	yes	—
70	C₂²×D₁₇₂	—	2	8	no	—
71	C₂²×D₁₇₂	C₂³	1	2	yes	—
72	C₂²×D₁₇₂	C₂³	1	2	yes	—
73	C₂²×D₁₇₂	C₂³	1	8	yes	—
74	C₂²×C₂²⋊D₄₃	C₂³	1	8	yes	—
75	C₂³×Dic₄₃	C₂³	1	2	yes	—
76	C₂³×Dic₄₃	C₂³	1	4	yes	—
77	C₂²×C₄×D₄₃	C₂³	1	8	yes	—
78	#13063324	C₂³	1	16	yes	complemented
79	#13063321	C₂³	1	16	yes	—
80	#13063320	C₂³	1	64	yes	complemented
81	#13063320	C₂³	1	64	yes	complemented
82	#13063316	C₂³	1	16	yes	complemented
83	#13063314	C₂³	1	16	yes	—
84	#13063314	C₂³	1	32	yes	—
85	#13063314	C₂³	1	16	yes	—
86	#13063314	C₂³	1	16	yes	—
87	#13063311	C₂³	1	64	yes	complemented
88	#13063309	C₂³	1	64	yes	complemented
89	#13063307	C₂³	1	64	yes	complemented
90	#13063305	C₂³	1	64	yes	complemented
91	#13063302	C₂³	1	32	yes	—
92	#13063299	C₂³	1	32	yes	—
93	#13063293	C₂³	1	32	yes	—
94	Q₈×Dic₄₃	C₂³	1	16	yes	complemented
95	Q₈×Dic₄₃	C₂³	1	32	yes	complemented
96	Q₈×Dic₄₃	C₂³	1	32	yes	complemented
97	C₄×Dic₈₆	C₂³	1	32	yes	complemented
98	C₄×D₁₇₂	C₂³	1	32	yes	—
99	D₄×Dic₄₃	C₂³	1	32	yes	—
100	D₄×Dic₄₃	C₂³	1	16	yes	complemented
101	#13063287	C₂³	1	32	yes	—
102	(C₂²⋊D₄₃)⋊C₄	C₂³	1	64	yes	complemented
103	#13063284	C₂³	1	32	yes	—
104	#13063284	C₂³	1	8	yes	—
105	#13063284	C₂³	1	8	yes	—
106	#13063284	C₂³	1	16	yes	complemented
107	#13063283	C₂³	1	64	yes	complemented
108	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
109	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
110	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
111	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
112	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
113	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
114	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
115	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
118	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	32	yes	—
119	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
120	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
121	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
122	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
123	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	—
124	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
125	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
126	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
127	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
128	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
129	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
130	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
131	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
132	C₂×C₄×Dic₄₃	C₂³	1	16	yes	complemented
133	C₂×#41×C₄₃	—	2	8	no	—
134	C₂×#41×C₄₃	C₂³	1	8	yes	—
135	C₂²×Q₈×C₄₃	—	2	8	no	—
136	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
137	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₄₃	C₂³	1	8	yes	—
140	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₄₃	C₂³	1	16	yes	complemented
146	#124×C₄₃	C₂³	1	16	yes	complemented
147	#123×C₄₃	C₂³	1	32	yes	—
148	C₂²⋊Q₈×C₄₃	C₂³	1	32	yes	complemented
149	#117×C₄₃	C₂³	1	8	yes	—
150	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
152	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
154	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
155	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
156	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂³×D₄₃	—	2	8	no	—
158	C₂³×D₄₃	—	4	8	no	—
159	C₂³×D₄₃	C₂⁴	1	4	yes	—
160	C₂³×D₄₃	C₂⁴	1	8	yes	—
161	#41×C₄₃	—	2	32	no	—
162	C₂×Q₈×C₄₃	—	2	8	no	—
163	C₂×Q₈×C₄₃	—	2	8	no	—
164	C₂×Q₈×C₄₃	—	2	32	no	—
165	C₂×Q₈×C₄₃	—	2	4	no	—
166	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
167	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
168	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
169	C₂×D₄×C₄₃	—	2	4	no	—
170	C₂×D₄×C₄₃	—	2	8	no	—
171	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
172	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₄₃	—	2	8	no	—
174	C₂²×C₄×C₄₃	—	2	8	no	—
175	C₂²×C₄×C₄₃	#41	1	8	yes	—
176	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
184	C₂×C₂²⋊D₄₃	—	4	16	no	—
185	C₂×C₂²⋊D₄₃	C₂⁴	1	32	yes	—
186	C₂²×Dic₄₃	—	4	4	no	—
187	C₂²×Dic₄₃	—	4	8	no	—
188	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
189	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
190	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
191	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
192	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
193	C₂²×Dic₄₃	C₂⁴	1	16	yes	—
194	C₂×D₁₇₂	—	2	8	no	—
195	C₂×D₁₇₂	—	2	8	no	—
196	C₂×D₁₇₂	—	2	32	no	—
197	C₂×D₁₇₂	C₂⁴	1	8	yes	—
198	C₂×D₁₇₂	C₂⁴	1	8	yes	—
199	C₂×C₄×D₄₃	—	4	16	no	—
200	C₂×C₄×D₄₃	C₂⁴	1	32	yes	—
201	C₂×Dic₈₆	—	4	8	no	—
202	C₂×Dic₈₆	C₂⁴	1	16	yes	—
203	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
204	C₄⋊C₄×C₄₃	C₂⁴	1	32	yes	—
205	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
206	C₂²⋊C₄×C₄₃	C₂⁴	1	32	yes	—
207	C₄²×C₄₃	C₂⁴	1	8	yes	—
208	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
209	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
210	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
211	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
212	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
213	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
214	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
215	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
216	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
217	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
218	C₄⋊Dic₄₃	C₂⁴	1	32	yes	—
219	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
220	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
221	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
222	C₄×Dic₄₃	C₂⁴	1	4	yes	—
223	C₄×Dic₄₃	C₂⁴	1	4	yes	—
224	C₄×Dic₄₃	C₂⁴	1	8	yes	—
225	C₄×Dic₄₃	C₂⁴	1	16	yes	—
226	C₄×Dic₄₃	C₂⁴	1	8	yes	—
227	C₄×Dic₄₃	C₂⁴	1	32	yes	—
228	C₄×Dic₄₃	C₂⁴	1	8	yes	—
229	C₂³×C₄₃	—	2	4	no	—
230	C₂³×C₄₃	—	2	4	no	—
231	C₂³×C₄₃	—	2	8	no	—
232	C₂³×C₄₃	C₂×#41	1	4	yes	—
233	C₂³×C₄₃	C₂⁵	1	4	yes	—
234	C₂³×C₄₃	C₂⁵	1	2	yes	—
235	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
236	C₂²×D₄₃	—	2	8	no	—
237	C₂²×D₄₃	—	2	16	no	—
238	C₂²×D₄₃	—	2	16	no	—
239	C₂²×D₄₃	—	4	16	no	—
240	C₂²×D₄₃	—	8	16	no	—
241	C₂²×D₄₃	C₂⁵	1	8	yes	—
242	Q₈×C₄₃	—	2	16	no	—
243	Q₈×C₄₃	—	2	16	no	—
244	Q₈×C₄₃	—	2	8	no	—
245	D₄×C₄₃	—	2	16	no	—
246	D₄×C₄₃	—	2	8	no	—
247	C₂×C₄×C₄₃	—	2	4	no	—
248	C₂×C₄×C₄₃	—	2	16	no	—
249	C₂×C₄×C₄₃	—	2	8	no	—
250	C₂×C₄×C₄₃	—	2	8	no	—
251	C₂×C₄×C₄₃	—	2	16	no	—
252	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
253	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
254	C₂×C₄×C₄₃	C₂×#41	1	16	yes	—
255	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
256	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
257	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
258	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
259	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
260	C₂²⋊D₄₃	—	4	32	no	—
261	C₂×Dic₄₃	—	2	4	no	—
262	C₂×Dic₄₃	—	2	8	no	—
263	C₂×Dic₄₃	—	2	8	no	—
264	C₂×Dic₄₃	—	2	4	no	—
265	C₂×Dic₄₃	—	4	8	no	—
266	C₂×Dic₄₃	—	4	16	no	—
267	C₂×Dic₄₃	C₂⁵	1	4	yes	—
268	C₂×Dic₄₃	C₂⁵	1	8	yes	—
269	C₂×Dic₄₃	C₂⁵	1	8	yes	—
270	C₂×Dic₄₃	C₂⁵	1	4	yes	—
271	D₁₇₂	—	2	16	no	—
272	D₁₇₂	—	2	16	no	—
273	C₄×D₄₃	—	4	32	no	—
274	Dic₈₆	—	4	16	no	—
275	C₂×#3510	—	43	1	no	maximal, Sylow
276	C₂²×C₄₃	—	2	4	no	—
277	C₂²×C₄₃	—	2	8	no	—
278	C₂²×C₄₃	—	2	4	no	—
279	C₂²×C₄₃	—	2	8	no	—
280	C₂²×C₄₃	—	4	8	no	—
281	C₂²×C₄₃	C₂²×#41	1	4	yes	—
282	C₂²×C₄₃	C₂²×#41	1	2	yes	—
283	C₂²×C₄₃	#585	1	4	yes	—
284	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
285	C₂×D₄₃	—	2	8	no	—
286	C₂×D₄₃	—	2	16	no	—
287	C₂×D₄₃	—	4	16	no	—
288	C₂×D₄₃	—	8	16	no	—
289	C₄×C₄₃	—	2	4	no	—
290	C₄×C₄₃	—	2	8	no	—
291	C₄×C₄₃	—	2	8	no	—
292	C₄×C₄₃	C₂²×#41	1	4	yes	—
293	C₄×C₄₃	C₂²×#41	1	4	yes	—
294	Dic₄₃	—	2	4	no	—
295	Dic₄₃	—	2	8	no	—
296	Dic₄₃	—	2	8	no	—
297	Dic₄₃	—	2	4	no	—
298	#3510	—	43	32	no	—
299	C₂×#559	—	43	4	no	—
300	C₂×#556	—	43	4	no	—
301	C₂×#551	—	43	8	no	—
302	C₂×#542	—	43	4	no	—
303	C₂×#536	D₄₃	1	1	yes	characteristic, complemented
304	C₂×#535	—	43	1	no	—
305	C₂×#533	—	43	1	no	—
306	C₂×#529	—	43	4	no	—
307	C₂²×#124	—	43	1	no	—
308	C₂×#519	—	43	1	no	—
309	C₂×#518	—	43	1	no	—
310	C₂×C₄×#41	—	43	1	no	—
311	C₂×C₄₃	—	2	4	no	—
312	C₂×C₄₃	—	4	4	no	—
313	C₂×C₄₃	#3510	1	4	yes	complemented
314	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
315	C₂×C₄₃	C₂×#585	1	2	yes	—
316	D₄₃	—	4	8	no	—
317	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
318	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
319	C₂³×D₄	—	43	1	no	—
320	#559	—	43	64	no	—
321	#556	—	43	64	no	—
322	#551	—	43	128	no	—
323	#542	—	43	64	no	—
324	#536	C₂×D₄₃	1	16	yes	complemented
325	#535	—	43	16	no	—
326	#533	—	43	16	no	—
327	C₂×C₄⋊Q₈	—	43	2	no	—
328	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	complemented
329	C₂×#127	—	43	2	no	—
330	#529	—	43	64	no	—
331	C₂×#126	—	43	8	no	—
332	C₂×#126	—	43	8	no	—
333	C₂×#125	—	43	2	no	—
334	C₂×#124	—	43	2	no	—
335	C₂×#124	—	43	2	no	—
336	C₂×#124	—	43	4	no	—
337	C₂×#124	—	43	16	no	—
338	C₂×#124	—	43	2	no	—
339	C₂×#124	—	43	8	no	—
340	C₂×#124	C₂×D₄₃	1	2	yes	complemented
341	C₂×#123	—	43	8	no	—
342	C₂×#123	—	43	8	no	—
343	C₂×#123	C₂×D₄₃	1	4	yes	—
344	C₂×C₂²⋊Q₈	—	43	8	no	—
345	C₂×C₂²⋊Q₈	—	43	4	no	—
346	C₂×C₂²⋊Q₈	C₂×D₄₃	1	4	yes	complemented
347	C₂×#121	—	43	4	no	—
348	C₂×#120	—	43	4	no	—
349	#519	—	43	16	no	—
350	#518	—	43	16	no	—
351	C₄×#41	—	43	16	no	—
352	C₂×C₄×Q₈	—	43	2	no	—
353	C₂×C₄×Q₈	—	43	4	no	—
354	C₂×C₄×Q₈	—	43	4	no	—
355	C₂×C₄×Q₈	—	43	4	no	—
356	C₂×C₄×D₄	—	43	4	no	—
357	C₂×C₄×D₄	—	43	2	no	—
358	C₂×C₄×D₄	—	43	4	no	—
359	C₂×C₄×D₄	—	43	8	no	—
360	C₂×C₄×D₄	—	43	4	no	—
361	C₂×#117	—	43	1	no	—
362	C₂×#117	—	43	1	no	—
363	C₂×#117	—	43	4	no	—
364	C₂×#117	—	43	2	no	—
365	C₂×#117	—	43	8	no	—
366	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	—	43	4	no	—
368	C₂²×C₂²⋊C₄	—	43	4	no	—
369	C₂²×C₄²	—	43	1	no	—
370	C₂²×C₄²	—	43	2	no	—
371	C₄₃	C₂×#3510	1	1	yes	characteristic, complemented, Sylow
372	C₂⁵	—	43	2	no	—
373	C₂×#41	—	2	8	no	—
374	C₂×#41	C₂²×D₄₃	1	8	yes	—
375	C₂²×Q₈	—	2	8	no	—
376	C₂²×Q₈	—	43	4	no	—
377	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
378	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
379	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
380	C₂²×Q₈	C₂²×D₄₃	1	8	yes	—
381	C₂²×D₄	—	43	8	no	—
382	C₂²×D₄	—	43	2	no	—
383	C₂²×D₄	—	43	2	no	—
384	C₂²×D₄	—	43	8	no	—
385	C₂²×D₄	—	86	8	no	—
386	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
387	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
388	C₂³×C₄	—	43	2	no	—
389	C₂³×C₄	—	43	4	no	—
390	C₂³×C₄	—	43	8	no	—
391	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
392	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
393	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
394	C₄⋊Q₈	—	43	16	no	—
395	C₄⋊Q₈	C₂²×D₄₃	1	16	yes	complemented
396	#127	—	43	16	no	—
397	#126	—	43	64	no	—
398	#126	—	43	64	no	—
399	#125	—	43	16	no	—
400	#124	—	43	16	no	—
401	#124	—	43	16	no	—
402	#124	—	43	32	no	—
403	#124	—	43	16	no	—
404	#124	—	43	64	no	—
405	#124	C₂²×D₄₃	1	16	yes	complemented
406	#123	—	43	64	no	—
407	#123	—	43	64	no	—
408	#123	C₂²×D₄₃	1	32	yes	—
409	C₂²⋊Q₈	—	43	64	no	—
410	C₂²⋊Q₈	—	43	32	no	—
411	C₂²⋊Q₈	C₂²×D₄₃	1	32	yes	complemented
412	#121	—	43	32	no	—
413	#120	—	43	32	no	—
414	C₄×Q₈	—	43	16	no	—
415	C₄×Q₈	—	43	32	no	—
416	C₄×Q₈	—	43	32	no	—
417	C₄×Q₈	—	43	32	no	—
418	C₄×D₄	—	43	32	no	—
419	C₄×D₄	—	43	16	no	—
420	C₄×D₄	—	43	32	no	—
421	C₄×D₄	—	43	64	no	—
422	C₄×D₄	—	43	32	no	—
423	#117	—	43	8	no	—
424	#117	—	43	16	no	—
425	#117	—	43	8	no	—
426	#117	—	43	32	no	—
427	#117	—	43	64	no	—
428	#117	C₂²×D₄₃	1	8	yes	—
429	C₂×C₄⋊C₄	—	43	4	no	—
430	C₂×C₄⋊C₄	—	43	2	no	—
431	C₂×C₄⋊C₄	—	43	4	no	—
432	C₂×C₄⋊C₄	—	43	2	no	—
433	C₂×C₄⋊C₄	—	43	8	no	—
434	C₂×C₄⋊C₄	—	43	4	no	—
435	C₂×C₄⋊C₄	—	43	4	no	—
436	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
437	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
438	C₂×C₂²⋊C₄	—	43	2	no	—
439	C₂×C₂²⋊C₄	—	43	2	no	—
440	C₂×C₂²⋊C₄	—	43	4	no	—
441	C₂×C₂²⋊C₄	—	43	8	no	—
442	C₂×C₂²⋊C₄	—	43	8	no	—
443	C₂×C₂²⋊C₄	—	43	8	no	—
444	C₂×C₂²⋊C₄	—	43	32	no	—
445	C₂×C₂²⋊C₄	—	43	8	no	—
446	C₂×C₂²⋊C₄	—	43	32	no	—
447	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
449	C₂×C₄²	—	43	2	no	—
450	C₂×C₄²	—	43	8	no	—
451	C₂×C₄²	—	43	4	no	—
452	C₂×C₄²	—	43	1	no	—
453	C₂×C₄²	—	43	2	no	—
454	C₂×C₄²	—	43	2	no	—
455	C₂×C₄²	—	43	8	no	—
456	C₂×C₄²	—	43	16	no	—
457	C₂×C₄²	—	43	1	no	—
458	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
459	C₂⁴	—	43	4	no	—
460	C₂⁴	—	43	8	no	—
461	C₂⁴	—	86	8	no	—
462	C₂⁴	—	172	8	no	—
463	C₂⁴	C₂³×D₄₃	1	2	yes	—
464	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
465	#41	—	2	32	no	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	32	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	43	16	no	—
471	C₂×Q₈	—	172	8	no	—
472	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
473	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
474	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	43	32	no	—
478	C₂×D₄	—	43	8	no	—
479	C₂×D₄	—	43	8	no	—
480	C₂×D₄	—	86	8	no	—
481	C₂×D₄	—	86	8	no	—
482	C₂×D₄	—	86	32	no	—
483	C₂×D₄	—	172	16	no	—
484	C₂×D₄	C₂³×D₄₃	1	8	yes	—
485	C₂×D₄	C₂³×D₄₃	1	4	yes	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	43	4	no	—
489	C₂²×C₄	—	43	2	no	—
490	C₂²×C₄	—	43	4	no	—
491	C₂²×C₄	—	43	2	no	—
492	C₂²×C₄	—	43	8	no	—
493	C₂²×C₄	—	43	16	no	—
494	C₂²×C₄	—	43	32	no	—
495	C₂²×C₄	—	172	16	no	—
496	C₂²×C₄	—	172	8	no	—
497	C₂²×C₄	—	172	4	no	—
498	C₂²×C₄	#10621900	1	8	yes	—
499	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
500	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
501	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
502	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
503	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
504	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
505	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
507	C₄⋊C₄	—	43	16	no	—
508	C₄⋊C₄	—	43	8	no	—
509	C₄⋊C₄	—	43	16	no	—
510	C₄⋊C₄	—	43	8	no	—
511	C₄⋊C₄	—	43	32	no	—
512	C₄⋊C₄	—	43	16	no	—
513	C₄⋊C₄	—	43	16	no	—
514	C₄⋊C₄	C₂³×D₄₃	1	32	yes	—
515	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
516	C₂²⋊C₄	—	43	8	no	—
517	C₂²⋊C₄	—	43	8	no	—
518	C₂²⋊C₄	—	43	16	no	—
519	C₂²⋊C₄	—	43	32	no	—
520	C₂²⋊C₄	—	43	32	no	—
521	C₂²⋊C₄	—	43	32	no	—
522	C₂²⋊C₄	—	43	32	no	—
523	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
524	C₂²⋊C₄	C₂³×D₄₃	1	32	yes	—
525	C₄²	—	43	4	no	—
526	C₄²	—	43	8	no	—
527	C₄²	—	43	16	no	—
528	C₄²	—	43	4	no	—
529	C₄²	—	43	8	no	—
530	C₄²	—	43	32	no	—
531	C₄²	—	43	8	no	—
532	C₄²	C₂³×D₄₃	1	8	yes	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	43	8	no	—
537	C₂³	—	86	16	no	—
538	C₂³	—	86	8	no	—
539	C₂³	—	86	16	no	—
540	C₂³	—	344	16	no	—
541	C₂³	—	172	16	no	—
542	C₂³	C₂×#10621900	1	4	yes	—
543	C₂³	C₂⁴×D₄₃	1	4	yes	—
544	C₂³	C₂⁴×D₄₃	1	2	yes	—
545	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
546	Q₈	—	2	16	no	—
547	Q₈	—	2	16	no	—
548	Q₈	—	2	8	no	—
549	Q₈	—	172	16	no	—
550	D₄	—	2	16	no	—
551	D₄	—	2	8	no	—
552	D₄	—	86	16	no	—
553	D₄	—	86	16	no	—
554	D₄	—	172	32	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	43	4	no	—
561	C₂×C₄	—	43	8	no	—
562	C₂×C₄	—	43	8	no	—
563	C₂×C₄	—	43	4	no	—
564	C₂×C₄	—	86	8	no	—
565	C₂×C₄	—	86	4	no	—
566	C₂×C₄	—	86	4	no	—
567	C₂×C₄	—	86	8	no	—
568	C₂×C₄	—	172	32	no	—
569	C₂×C₄	—	172	16	no	—
570	C₂×C₄	—	172	8	no	—
571	C₂×C₄	C₂×#10621900	1	4	yes	—
572	C₂×C₄	C₂×#10621900	1	4	yes	—
573	C₂×C₄	C₂×#10621900	1	16	yes	—
574	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
575	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
576	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
577	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
578	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	86	8	no	—
585	C₂²	—	86	16	no	—
586	C₂²	—	344	16	no	—
587	C₂²	—	172	16	no	—
588	C₂²	C₂²×#10621900	1	4	yes	—
589	C₂²	C₂²×#10621900	1	2	yes	—
590	C₂²	#14583736	1	4	yes	—
591	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	—	86	8	no	—
596	C₄	—	86	4	no	—
597	C₄	—	86	4	no	—
598	C₄	—	86	8	no	—
599	C₄	C₂²×#10621900	1	4	yes	—
600	C₄	C₂²×#10621900	1	4	yes	—
601	C₂	—	2	4	no	—
602	C₂	—	4	4	no	—
603	C₂	—	172	8	no	—
604	C₂	#19148494	1	4	yes	direct product factor
605	C₂	C₂³×#10621900	1	1	yes	characteristic
606	C₂	C₂×#14583736	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#536	C₂
socle	C₂³×C₄₃	C₂⁵
prime radical	C₂×#14583463	C₂
hypercenter	C₂×#536	D₄₃
hypocenter	C₄₃	C₂×#3510
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #19148494	C₂	direct (N × H)
2. C₂×#14583631	C₂	semidirect
3. C₂×#14583623	C₂	semidirect
4. C₂×#14583572	C₂	semidirect
5. C₂×#14583522	C₂	semidirect
7. C₂×#14583452	C₂	semidirect
8. C₂×#14583435	C₂	semidirect
9. C₂²×#13063314	C₂	semidirect
10. C₂×#14583377	C₂	semidirect
11. C₂×#14583373	C₂	semidirect
12. C₂×#41×Dic₄₃	C₂	semidirect
13. C₂×C₄₃×#536	C₂	semidirect
15. #14583631	C₂²	semidirect
16. #14583623	C₂²	semidirect
17. #14583572	C₂²	semidirect
18. #14583522	C₂²	semidirect
20. #14583452	C₂²	semidirect
21. C₂×#13063324	C₂²	semidirect
23. #14583435	C₂²	semidirect
24. C₂×#13063320	C₂²	semidirect
25. C₂×#13063320	C₂²	semidirect
26. C₂×#13063316	C₂²	semidirect
31. C₂×#13063314	C₂²	semidirect
32. C₂×#13063311	C₂²	semidirect
33. C₂×#13063309	C₂²	semidirect
34. C₂×#13063307	C₂²	semidirect
35. C₂×#13063305	C₂²	semidirect
39. #14583377	C₂²	semidirect
40. #14583373	C₂²	semidirect
41. #41×Dic₄₃	C₂²	semidirect
42. C₂×Q₈×Dic₄₃	C₂²	semidirect
43. C₂×Q₈×Dic₄₃	C₂²	semidirect
44. C₂×Q₈×Dic₄₃	C₂²	semidirect
45. C₂×C₄×Dic₈₆	C₂²	semidirect
48. C₂×D₄×Dic₄₃	C₂²	semidirect
50. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
54. C₂×#13063284	C₂²	semidirect
55. C₂×#13063283	C₂²	semidirect
59. C₂²×C₄×Dic₄₃	C₂²	semidirect
62. C₄₃×#536	C₂²	semidirect
63. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
64. C₂×#124×C₄₃	C₂²	semidirect
66. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
78. #13063324	C₂³	semidirect
80. #13063320	C₂³	semidirect
81. #13063320	C₂³	semidirect
82. #13063316	C₂³	semidirect
87. #13063311	C₂³	semidirect
88. #13063309	C₂³	semidirect
89. #13063307	C₂³	semidirect
90. #13063305	C₂³	semidirect
94. Q₈×Dic₄₃	C₂³	semidirect
95. Q₈×Dic₄₃	C₂³	semidirect
96. Q₈×Dic₄₃	C₂³	semidirect
97. C₄×Dic₈₆	C₂³	semidirect
100. D₄×Dic₄₃	C₂³	semidirect
102. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
106. #13063284	C₂³	semidirect
107. #13063283	C₂³	semidirect
132. C₂×C₄×Dic₄₃	C₂³	semidirect
145. C₄⋊Q₈×C₄₃	C₂³	semidirect
146. #124×C₄₃	C₂³	semidirect
148. C₂²⋊Q₈×C₄₃	C₂³	semidirect
303. C₂×#536	D₄₃	semidirect
313. C₂×C₄₃	#3510	semidirect
324. #536	C₂×D₄₃	semidirect
328. C₂×C₄⋊Q₈	C₂×D₄₃	semidirect
340. C₂×#124	C₂×D₄₃	semidirect
346. C₂×C₂²⋊Q₈	C₂×D₄₃	semidirect
371. C₄₃	C₂×#3510	semidirect
395. C₄⋊Q₈	C₂²×D₄₃	semidirect
405. #124	C₂²×D₄₃	semidirect
411. C₂²⋊Q₈	C₂²×D₄₃	semidirect
604. C₂	#19148494	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19148494	2
C₂×#14583631	2
C₂×#14583623	2
C₂×#14583572	2
C₂×#14583522	2
C₂×#14583463	2
C₂×#14583452	2
C₂×#14583435	2
C₂²×#13063314	2
C₂×#14583377	2
C₂×#14583373	2
C₂×#41×Dic₄₃	2
C₂×C₄₃×#536	2
C₂×#3510	43

Subgroups — C2×#19148494 #26005091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148494 #26005091